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Stability analysis of second- and fourth-order finite-difference modelling of wave propagation in orthotropic media

Veres, Istvan (2010) Stability analysis of second- and fourth-order finite-difference modelling of wave propagation in orthotropic media. Ultrasonics, 50 (3). pp. 431-438. ISSN 0041-624X

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    Abstract

    The stability of the finite-difference approximation of elastic wave propagation in orthotropic homogeneous media in the three-dimensional case is discussed. The model applies second- and fourth-order finite-difference approaches with staggered grid and stress-free boundary conditions in the space domain and second-order finite-difference approach in the time domain. The numerical integration of the wave equation by central differences is conditionally stable and the corresponding stability criterion for the time domain discretisation has been deduced as a function of the material properties and the geometrical discretization. The problem is discussed by applying the method of VonNeumann. Solutions and the calculation of the critical time steps is presented for orthotropic material in both the second- and fourth-order case. The criterion is verified for the special case of isotropy and results in the well-known formula from the literature. In the case of orthotropy the method was verified by long time simulations and by calculating the total energy of the system.

    Item type: Article
    ID code: 25789
    Keywords: finite differences, numerical simulation, stability analysis, Electrical engineering. Electronics Nuclear engineering, Acoustics and Ultrasonics
    Subjects: Technology > Electrical engineering. Electronics Nuclear engineering
    Department: Faculty of Engineering > Electronic and Electrical Engineering
    Related URLs:
    Depositing user: Dr James Windmill
    Date Deposited: 07 Jul 2010 10:25
    Last modified: 27 Mar 2014 19:28
    URI: http://strathprints.strath.ac.uk/id/eprint/25789

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